CG4AI is a column generation framework that trains AI models while enforcing linear constraints on their outputs. It constructs a convex combination of models, using a master linear program to set mixture weights and a pricing subproblem to generate new models guided by dual variables, focusing on the most violated constraints. The method is applied to MNIST digit classification—demonstrating constraint learning, adversarial robustness, error correction, and output relabeling—and to multi‑commodity flow routing, achieving feasible predictors with higher accuracy than single‑model baselines.
arXiv:2607. 13373v1 Announce Type: cross Abstract: Column generation (CG) is central to many large-scale optimization algorithms, including branch-price-and-cut methods for vehicle routing problems, but unstable dual solutions can substantially slow its convergence.
arXiv:2606. 13803v1 Announce Type: new Abstract: Enforcing functional inequality constraints such as monotonicity and convexity in neural networks is a fundamental challenge in many industrial and scientific applications.
arXiv:2512.20270v2 Announce Type: replace-cross Abstract: Many engineering tasks require solving families of nonlinear constrained optimization problems, parametrized in setting-specific variables. T...
arXiv:2505.05261v4 Announce Type: replace-cross Abstract: Two-stage stochastic programming (2SP) offers a basic framework for modelling decision-making under uncertainty, yet scalability remains a ch...
arXiv:2605.24437v2 Announce Type: replace Abstract: We present a novel framework for embedding hard constraint satisfaction into neural network (NN) architectures, specifically feedforward neural net...
The article "Constraint Learning by Optimizing over Trained Neural Networks: A Pragmatic Tutorial" discusses the emerging paradigm of embedding trained machine learning models, particularly neural networks, into optimization problems. It explains how constraints can be learned from data or objectives approximated to simplify models, while addressing challenges of size and speed. The tutorial offers practical guidance and demonstrates benefits through a case study that shows smaller, sparser networks can improve efficiency.
arXiv:2608. 09707v1 Announce Type: cross Abstract: Embedding trained neural networks as surrogates within optimisation problems is an established practice in operations research.
arXiv:2605.18618v3 Announce Type: replace-cross Abstract: Constrained Machine Learning (CML) enables fairness-aware training, physics-informed neural networks, and integration of symbolic domain know...
HUANet is a deep neural network architecture that unrolls the Alternating Direction Method of Multipliers (ADMM) into a trainable model for accelerating parametric constrained convex optimization. It embeds a hard‑constrained neural network in each ADMM iteration, using a differentiable correction stage to enforce affine equalities of the primal subproblem. The method also incorporates first‑order optimality conditions into a self‑supervised training loss, and numerical experiments on benchmark problems and a control application demonstrate its effectiveness in speeding up constrained convex optimization.
arXiv:2609.34628v2 Announce Type: replace-cross Abstract: Neural network verification (NNV) formally verifies that a network satisfies a specified property for all inputs within a defined region. Mod...
arXiv:2608. 02343v1 Announce Type: cross Abstract: Many operational problems are constrained sequential decision processes with large, combinatorial action spaces and interdependent feasibility constraints.
The paper introduces ReMILP, a reformulation‑contrastive learning framework that uses self‑supervision from equivalent formulations of mixed‑integer linear programs (MILPs). By distinguishing re‑descriptions and substitutions, the method trains a graph neural network and a hypernetwork to predict how variable embeddings transform under changes of variables, achieving invariance and equivariance without solver‑derived labels. The learned representations prove useful for tasks such as binary solution, constraint activity, and integrality gap prediction, and serve as a strong initialization for fine‑tuning.